\(£\)  being the Lie-derivative, a constant and a smooth vector field are denoted by \(\beta _2\)  and \(X_1\) , respectively, while the Ricci tensor is denoted by \(\mathcal {S}\) . The Ricci flow equation which was presented by Hamilton[1]} is defined by
\(\frac{\partial }{\partial t}g = -2\mathcal {S}.\) 
